Methods for Detecting the Flight Path of Projectiles

ABSTRACT

Methods for detecting the flight path of projectiles involve a sequence of N target detections that include detecting the measured velocities and azimuthal angle bearings of the projectile along the flight path of the projectile by Doppler radar at the times tn, wherein n=1 . . . N, and determining the flight path and the direction of motion of the projectile are from these measurements. The measurements are adapted in a first nonlinear parameter fit to an analytical relationship of the time curve of the radial velocity of the projectile while the projectile passes through the detection range of the radar and so that the absolute projectile velocity, minimum distance of the project flight path from the radar, time at which the projectile passes the point having the minimum distance, flight path direction in azimuth, and flight path direction in elevation can be estimated.

BACKGROUND AND SUMMARY OF THE INVENTION

Exemplary embodiments of the present invention relate to methods fordetecting the trajectories of projectiles.

Soldiers in action in crisis regions are constantly at threat of beingfired at by hand weapons from behind (e.g. by so-called snipers).

Methods are already known for deriving information regarding positionand direction from which the shot is fired. These methods involveacoustic sensors that determine the position of the shooters from themuzzle blast. Such acoustic sensors are disadvantageous because theyrequire multiple spatially distributed and networked supportingpositions (microphones). Moreover, such acoustic systems can easily bedisturbed by ambient noise. Accordingly, acoustic sensors cannot be usedon travelling or flying platforms or can only be used thereon in alimited manner.

Optical methods are also known for attempting to discover the opticalsights of sharpshooter weapons. The application area of these systems isstrictly limited because the firing of other hand weapons cannot bedetected. These systems are also significantly adversely affected intheir efficiency by ambient influences such as light sources or dust.

German patent document DE 10 2006 006 983 A1 discloses a method fordetecting the trajectory and direction of motion of projectiles by meansof a coherent pulse Doppler radar. The measurement of distance to adetected object involves using the transition time of the echo pulse,while the projectile speed is advantageously determined by means of theDoppler frequency shift in the echo signal.

Another method for detecting the trajectory and direction of motion ofprojectiles is disclosed in the publication Allen, M. R.; Stoughton, R.B.; A Low Cost Radar Concept for Bullet Direction Finding Proceedings ofthe 1996 IEEE National Radar Conference, 13-16 May 1996, pp 202-207.

German patent document DE 40 12 247 A1 discloses a sensor system, withwhich the azimuth angle, elevation angle, radial distance and radialspeed of a target are measured.

German patent document DE 40 08 395 A1 discloses a monopulse radar fordetermining the azimuth, elevation and distance of a projectile.

Exemplary embodiments of the present invention provide a method that canreliably and universally detect the trajectory and direction of motionof projectiles.

In order to determine the trajectory parameters of projectiles (e.g.rifle bullets), it is assumed that they travel in a straight line andthe speed in the detection region is constant. These assumptions arepermissible in a number of applications, in which it is a case ofdetecting the penetration of projectiles into a protection zone and thedetermination of the direction from which the shot originated. Onlyeither the direction in the plane (azimuth) or in addition the elevationdirection is of interest here.

A continuous wave Doppler radar with the capability for indicating abearing can be advantageously used as a sensor in the present invention.The angular resolution can be achieved either with a plurality ofreceiving antennas or sending/receiving antennas with a directionaleffect or with digital beam forming (DBF). The analysis of the Dopplersignal enables the measurement of the radial speed components of thedetected objects. The coverage of the radar sensor can be divided intoindividual angular segments, which are detected with spatiallydistributed individual and/or multiple sensors (sending/receivingmodules).

Because projectiles typically have a higher speed than all otherreflecting objects, the extraction of relevant signals can beaccomplished by spectral discrimination in the form of high passfiltering. This also applies if the sensor is disposed on a movingplatform (with a ground speed of up to about 300 km/h). This results ineffective clutter suppression.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

The invention is explained in detail below using figures. In thefigures:

FIG. 1 shows an exemplary time profile of the radial speed componentsduring a fly-past of the radar by a projectile,

FIG. 2 shows an exemplary time profile of the bearing in azimuth duringa lateral fly-past of the sensor by a projectile, and

FIG. 3 shows an exemplary expansion circuit of a Doppler radar sensorfor vertical bearing indication.

DETAILED DESCRIPTION

The time profile of the radial speed υ_(rad)(t) when passing through thedetection region of the sensor is—independently of the direction of theprojectile trajectory—described by the analytical relationship (1)below, which is also described in German patent document DE 29 42 355A1. It is assembled where appropriate from the data measured by thesensor within multiple antenna lobes—a sensor is understood to be acontinuous wave Doppler radar in the following:

$\begin{matrix}{{v_{{ra}\; d}(t)} = {\frac{v_{0}^{2} \cdot \left( {t_{d} - t} \right)}{\sqrt{{v_{0}^{2}\left( {t_{d} - t} \right)}^{2} + d^{2}}}.}} & (1)\end{matrix}$

Here υ0 designates the absolute projectile speed, d is the minimumdistance of the trajectory from the sensor (even if this point is neverin fact reached, because the projectile e.g. strikes the groundbeforehand), and td is the point in time at which the projectile passesthe point of closest approach (POCA). At the point the radial componentof the speed υrad(t) is reduced to zero, which is quite clearly shown.

In FIG. 1 such a profile of the radial speed is shown as an example forthe fly-past of a projectile with an airspeed of 800 m/sec at a distanceof 20 m from the sensor, wherein the POCA is achieved at point in timet=t_(d)=10 msec.

From a series of N target recordings provided by the Doppler sensor atthe points in time t_(n) with n=1 . . . N with measured speedsυ_(rad)(t_(n)), a non-linear parameter fit to the relationship (1) isperformed to determine the parameters υ₀, d and t_(d) or to estimatethem in the sense of a least mean square error (LMSE). Because there arethree unknowns, at least N=3 measurement points are necessary for this.Suitable algorithms for this are e.g. provided in the curve fittingtoolbox of MATLAB®.

The relationship of the bearing indication of the radar sensor to theprojectile trajectory in space can be derived from their vectorialdescription. The trajectory is given as a point-direction equation of astraight line with the speed vector u and the position vector at thePOCA d by the time function:

r(t)=d+v·(t−t _(d)),   (2)

which is identical to the direction vector between the sensor and theprojectile, if the radar sensor is assumed to be positionally fixed atthe origin of the coordinate system.

The Cartesian components of the direction vector r can be expressedusing the direction angle in azimuth α and elevation ε according to thespherical coordinate representation as:

$\begin{matrix}{{r = {\begin{pmatrix}r_{x} \\r_{y} \\r_{z}\end{pmatrix} = {{r}\begin{pmatrix}{\sin \; {\alpha \cdot \cos}\; ɛ} \\{\cos \; {\alpha \cdot \cos}\; ɛ} \\{\sin \; ɛ}\end{pmatrix}}}},} & (3)\end{matrix}$

wherein (2) is written as:

$\begin{matrix}{{{{r(t)}}\begin{pmatrix}{\sin \; {{\alpha (t)} \cdot \cos}\; {ɛ(t)}} \\{\cos \; {{\alpha (t)} \cdot \cos}\; {ɛ(t)}} \\{\sin \; {ɛ(t)}}\end{pmatrix}} = {{d\begin{pmatrix}{\sin \; {\alpha_{d} \cdot \cos}\; ɛ_{d}} \\{\cos \; {\alpha_{d} \cdot \cos}\; ɛ_{d}} \\{\sin \; ɛ_{d}}\end{pmatrix}} + {{v_{0}\begin{pmatrix}{\sin \; {\alpha_{0} \cdot \cos}\; ɛ_{0}} \\{\cos \; {\alpha_{0} \cdot \cos}\; ɛ_{0}} \\{\sin \; ɛ_{0}}\end{pmatrix}} \cdot \left( {t - t_{d}} \right)}}} & (4)\end{matrix}$

Here α(t) and ε(t) refer to the bearings of the radar sensor againsttime, α_(d) and ε_(d) to the angular directions at the POCA, and α₀ andε₀ to the directions of the trajectory in azimuth and elevation, i.e.the ultimately sought variables.

Forming a quotient from the x and y components of the trajectory (4)results in:

$\begin{matrix}{\frac{r_{x}(t)}{r_{y}(t)} = {\frac{\sin \; {\alpha (t)}}{\cos \; {\alpha (t)}} = {{\tan \; {\alpha (t)}} = \frac{{d\; \sin \; \alpha_{d}\; \cos \; ɛ_{d}} + {\sin \; \alpha_{0}\cos \; {ɛ_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}}{{d\; \cos \; \alpha_{d}\cos \; ɛ_{d}} + {\cos \; \alpha_{0}\cos \; {ɛ_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}}}}} & (5)\end{matrix}$

now independently of the distance |f(t)| to the projectile.

Turing first to the case that the radar sensor provides bearing valuesin azimuth α(t) for determining the trajectory direction in azimuth α₀.For this (5) can be put into the following form:

$\begin{matrix}{{\alpha (t)} = {\arctan \; {\frac{{d\; \sin \; \alpha_{d}k_{ɛ}} + {\sin \; {\alpha_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}}{{d\; \cos \; \alpha_{d}k_{ɛ}} + {\cos \; {\alpha_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}}.}}} & (6)\end{matrix}$

The elevation-dependent variables are combined into a single term:

$\begin{matrix}{k_{ɛ} = \frac{\cos \; ɛ_{d}}{\cos \; ɛ_{0}}} & (7)\end{matrix}$

For the case of a projectile with υ₀=800 m/sec, d=20 m and t_(d)=10msec, the time profile of the azimuth bearing α(t) is illustrated inFIG. 2 as an example. Simplified for the sake of interpretability, it isassumed that the projectile goes right past the sensor at the height ofthe sensor coming from the direction α₀=0° and ε₀=0°, and it is thuseasily shown that the following applies: α_(d)=90°, ε_(d)=0° and thusk_(ε)=1.

From a series of N radar sensor measured azimuth bearings α(t_(n)) atthe known points in time t_(n) with n=1 . . . N, the parameters α₀ andk_(ε) are determined using a second non-linear parameter fit torelationship (5). If there is no bearing in elevation, the variablek_(ε) is of no further use for the description of the trajectory. It canstill be determined that in (5) the influence of the elevation directionof the flight track ε₀ is separated from the determination of ε₀ andthus no systematic errors occur. In order to enable definite parameterextraction for ε₀ over the entire 360° range, the four quadrant arctangent can be adopted in (5) by taking into account the sign of thenumerator and denominator.

When carrying out the second parameter fit of the azimuth bearing valuesα(t_(n)) to (5), the values for υ₀, d and t_(d) are to be used, whichwere obtained during the first parameter fit to (1) using the speedmeasurement values. The value for α_(d), i.e. the azimuth bearing in thedirection of the POCA, is to be derived from the bearing valuesα(t_(n)). Because, however, at the POCA the radial components of thespeed are zero, there are no bearings in the immediate surroundings ofthe POCA because of the high pass clutter filtering. Instead aninterpolation of the series of measurement values α(t_(n)) at the pointin time t=t_(d) can be carried out: α_(d)=α(t_(d)).

In the case that the radar sensor also carries out elevation directionfinding besides the azimuth direction finding, the described method canbe expanded in an advantageous embodiment by a further step for flighttrack direction determination in elevation.

One approach is the combination of the vector components of (4) in theform:

$\begin{matrix}{{{\left( \frac{r_{x}(t)}{r_{y}(t)} \right)^{2} + \left( \frac{r_{x}(t)}{r_{y}(t)} \right)^{2}} = \frac{1}{\tan^{2}{ɛ(t)}}},} & (8)\end{matrix}$

which results in the following expression:

$\begin{matrix}{{\tan \; {ɛ(t)}} = {\frac{\left( {{d\; \sin \; ɛ_{d}} + {\sin \; {ɛ_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}} \right)}{\sqrt{\begin{matrix}{\left( {{d\; \cos \; \alpha_{d}\cos \; ɛ_{d}} + {\cos \; \alpha_{0}\cos \; {ɛ_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}} \right)^{2} +} \\\left( {{d\; \sin \; \alpha_{d}\cos \; ɛ_{d}} + {\sin \; \alpha_{0}\cos \; {ɛ_{0} \cdot {v_{0}\left( {t - t_{d}} \right)}}}} \right)^{2}\end{matrix}}}.}} & (9)\end{matrix}$

Also the target distance |r(t)| is no longer contained in therelationship and an analysis is possible purely on the basis of speedand bearing information.

By means of a third non-linear parameter fit the functional relationshipof the right side of (9), in which the elevation direction of the flighttrack ε₀ is the single remaining unknown variable, is adapted to theseries of values tan ε(t_(n)) formed from the measured bearing values.The previously determined variables d, υ₀, t_(d), α_(d) and α₀ are to beused as known, and ε_(d) is in turn to be determined by interpolationfrom the elevation bearing values ε(t_(n)) at the point in timet=t_(d):ε_(d)=ε(t_(d)).

According to the invention the following parameters are available todescribe the projectile's trajectory:

-   speed υ₀,-   minimum distance from the sensor d,-   point in time of the minimum distance t_(d),-   azimuth direction of the position with minimum distance (POCA)    α_(d),-   azimuth direction of the trajectory α₀.

In one particular embodiment of the invention, following a thirdparameter fit according to the features of claim 2 there are furtherparameters available for the description of the projectile's trajectory:

-   optional: elevation direction of the position with minimum distance    ε_(d),-   optional: elevation direction of the trajectory ε₀.

If it can be assumed that multiple projectiles can be simultaneouslypresent in the detection region of the sensor, time tracking can becarried out before the use of the parameter extraction based on (1), (6)and possibly (9) for segmentation of the measurement values for speedand bearing. The flight track parameters can then be determinedseparately for each segment (projectile). Under the assumption that suchscenarios only occur when firing salvos of projectiles, the parameterfit can be optimized to determine a single trajectory direction.

The bearing indication in the radar sensor can take place by means ofamplitude monopulse or phase monopulse. According to the invention thereis a simple alternative approach to expansion of the method by elevationdirection finding: The illuminator antenna is implemented in dual formwith a vertical angular offset between the antennas. Both antennastransmit simultaneously with slightly different frequencies f_(Tx1) andf_(Tx2)=f_(Tx1)+Δf (difference e.g. a few 100 Hz to a few kHz), whichcan be carried out in parallel in the entire signal path of the receiverincluding digitization. Both spectral lines only appear separately inthe Doppler analysis, their amplitude ratio in the sense of an amplitudemonopulse for the two mutually inclined illuminator antennas enablingelevation direction finding. On the receiver side there is thus noadditional hardware cost, which is clear on the transmitter side. Acircuit diagram showing the principle for said direction finding conceptis shown in FIG. 3.

When carrying out the Doppler analysis using a numerically efficient FFTthe following problem occurs: the time profile of the Doppler frequency(proportional to the radial speed components, see FIG. 1) allows onlycoherent integration times of typically a few milliseconds. Moreover,the resulting peak is spread within the Doppler spectrum (Doppler walk),so that there is no further integration gain in a conventional manner.However, extended integration times can be achieved according to theinvention by acquiring the Doppler signal as a sectional linear chirpand carrying out various hypothetical corrections with chirps ofdifferent lengths and gradients with rising and falling frequency bymultiplication in the time domain prior to the Doppler FFT. All of thesecorrected signal blocks are then subjected to the FFT, and in the caseof the correct correction approx. 10 dB higher integration gains andthus system sensitivities can be achieved. Alternatively, modified ISARprocessing is also conceivable, but this will not be discussed furtherhere.

Depending on the operating frequency of the radar sensor, the resultingrelevant Doppler shifts can be so small that they lie in the frequencyrange of low frequency noise (1/f-noise) or mechanical microphoniceffects. In this case a sinusoidal frequency modulation of thecontinuous wave transmission signal and an analysis of the receptionsignal can advantageously be used for the second harmonic of themodulation frequency [see, for example, M. Skolnik: Introduction toRadar Systems, ed. 2].

Finally, a typical system design for the radar sensor is mentioned as anexample:

-   working frequency in the K_(u)-Band (e.g. 16 GHz)-   four sensor segments (quadrants), each with a broad illuminator and    12 receiving antenna lobes in azimuth by means of DBF-   transmission power 1 W-   sampling frequency 300 kHz-   clutter high pass filter with 10 kHz corner frequency-   integration times 1 . . . 10 msec.

The foregoing disclosure has been set forth merely to illustrate theinvention and is not intended to be limiting. Since modifications of thedisclosed embodiments incorporating the spirit and substance of theinvention may occur to persons skilled in the art, the invention shouldbe construed to include everything within the scope of the appendedclaims and equivalents thereof.

1-12. (canceled)
 13. A method for the detection of the trajectory ofprojectiles, comprising: recording, by a Doppler radar, a series of Ntarget detections at points in time t_(n) with n=1 . . . N with measuredspeeds v_(rad)(t_(n)) and azimuthal angle bearings α(t_(n)) of theprojectile along the trajectory of the projectile; determining atrajectory and direction of motion of the projectile based on themeasured speeds υ_(rad)(t_(n)) and azimuthal angle bearings α(t_(n)) ofthe projectile along the trajectory of the projectile; estimatingabsolute projectile speed υ₀, minimum distance of projectile trajectoryfrom the radar d, and estimated point in time t_(d) at which theprojectile passes a point at a minimum distance d by adapting the speedmeasurements υ_(rad)(t_(n)) in a first non-linear parameter fit to ananalytical relationship of a time profile of the measured radial speedυ_(rad)(t) of the projectile when passing through the detection regionof the radar; estimating a trajectory direction in azimuth α₀ byadapting, in a second non-linear parameter fit, the measured azimuthalangle bearings α(t_(n)) to an analytical relationship of a time profileof the angular direction in azimuth α(t); and determining an azimuthdirection of the point α_(d) at the minimum distance of the projectiletrajectory from the Doppler radar by interpolating the series of themeasured azimuthal angle bearings α(t_(n)) at a point in time t=t_(d).14. The method as claimed in claim 13, wherein an additional series of Nangular bearings of the projectile in elevation ε(t_(n)) along thetrajectory of the projectile is recorded, a trajectory direction inelevation ε₀ is estimated by adapting the measurements in a thirdnon-linear parameter fit to an analytical relationship of the timeprofile of an angular direction in elevation ε(t), and determining theazimuth direction of a point ε_(d) at the minimum distance of theprojectile trajectory from the Doppler radar by interpolation of theseries of measurement values ε(t_(n)) at the point in time t=t_(d). 15.The method as claimed in claim 13, wherein the azimuthal angle bearingsare measured using a amplitude monopulse or phase monopulse.
 16. Themethod as claimed in claim 13, the measurement of speeds υ_(rad)(t_(n))is performed using a continuous wave Doppler radar, which comprises aplurality of transmission/reception modules for different spatial anglesectors.
 17. The method as claimed in claim 16, wherein thetransmission/reception module directionally selective antenna patternsare generated using digital beam forming.
 18. The method as claimed inclaim 16, a transmission signal of the continuous wave Doppler radar issubjected to a sinusoidal frequency modulation, wherein a frequencyrange is analyzed for a second harmonic of the modulation signal in aradar receiver.
 19. The method as claimed in claim 16, furthercomprising: band pass sampling a received signal to digitize thereceived signal.
 20. The method as claimed in claim 19, furthercomprising: integrating the received signal using FFT blocks withdifferent lengths to extend coherent integration time in Dopplerprocessing.
 21. The method as claimed in claim 20, wherein prior to theintegration of the received signal, a hypothetical correction of aprofile of the received signal is performed by multiplication with a setof linear frequency chirps of different ramp gradient and time duration.22. The method as claimed in claim 16, wherein a working frequency ofthe Doppler radar is in a K_(u) band or K band.
 23. The method asclaimed in 16, wherein a working frequency of the Doppler radar is in aS band or C band.
 24. The method as claimed in claim 16, wherein atransmission antenna of the transmission/reception module includes twoantennas having a vertical angular offset and transmittingsimultaneously with different frequencies f_(Tx1) andf_(Tx2)=f_(Tx1)+Δf, wherein the frequency difference Δf is from 100 Hzto 100 kHz.